The root-mean-square (rms) nuclear charge radius of 8 He, the most neutron-rich of all particlestable nuclei, has been determined for the first time to be 1.93(3) fm. In addition, the rms charge radius of 6 He was measured to be 2.068(11) fm, in excellent agreement with a previous result.The significant reduction in charge radius from 6 He to 8 He is an indication of the change in the correlations of the excess neutrons and is consistent with the 8 He neutron halo structure. The experiment was based on laser spectroscopy of individual helium atoms cooled and confined in a magneto-optical trap. Charge radii were extracted from the measured isotope shifts with the help of precision atomic theory calculations. * Electronic address: pmueller@anl.gov 1

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The results of an extended series of high-precision variational calculations for all states of helium up to n =10 and L=7 (excluding S states above n =2) are presented. Convergence of the nonrelativistic eigenvalues ranges from five parts in 10" for the 2P states to four parts in 10' for the 10K states. Relativistic and quantum electrodynamic corrections of order a, a, cz p/M, a (p/M), and a p/M are included and the required matrix elements listed for each state. For the 1s2p PJ states, the lowest-order spindependent matrix elements of the Breit interaction are determined to an accuracy of three parts in 10, which, together with higher-order corrections, would be sufficient to allow an improved measurement of the fine-structure constant. Methods of asymptotic analysis are extended to provide improved precision for the relativistic and relativistic-recoil corrections. A comparison with the variational results for the high-angular-momentum states shows that the "standard-atomic-theory" and "long-range-interaction" pictures discussed by Hessels et al. [Phys. Rev. Lett. 65, 2765 (1990)] come into agreement, thereby resolving what appeared to be a discrepancy. The comparison shows that the asymptotic expansions for the total energies are accurate to better than +100 Hz for L & 7, and results are presented for the 9L, 10L, and 10M states (i.e. , angular momentum L=8 and 9). Significant discrepancies with experiment persist for transitions among the n=10 states, which cannot be easily accommodated by supposed higher-order corrections or additional terms. Finally, the asymptotic analysis indicates that a revision to the quantum-defect method is required for the analysis of high-precision data.

We calculate very accurate ab initio ionization energies for both 4 He I and 3 He I as well as the isotope shifts for n = 1 to 10, L = 0 to 7 and combined these with precise laboratory data to produce a new table of levels for 4 He I and the first table for 3 He I. We adopted an experimental ionization potential of 5945 204 290 ± 33 MHz for 4 He I and derived 5944 890 770 ± 33 MHz for 3 He I. Additional calculations of the magnetic perturbations of 3 He I provide the hyperfine levels, which compare favourably with the available measurements. PACS Nos.: 31.30.Gs, 31.30.Jv Résumé : Nous avons fait un calcul ab initio de haute précision des énergies d'ionisation pour 4 He I et 3 He I, ainsi que des déplacements isotopiques pour n = 1 à 10 et L = 0 à 7 et avons combiné le tout avec des mesures précises en laboratoire , afin de produire une nouvelle table des niveaux de 4 He I et la toute première table pour 3 He I. Nous avons accepté la valeur expérimentale de 5945 204 290 ± 33 MHz pour le potentiel d'ionisation de 4 He I et fixé celui de 3 He I à 5944 890 770 ± 33 MHz. Des calculs additionnels sur les perturbations magnétiques dans 3 He I nous donnent des niveaux hyperfins qui se comparent favorablement avec les mesures publiées. [Traduit par la Rédaction]